Optimal. Leaf size=22 \[ \frac {3969 (3+x)^2 (-x+5 (-2+\log (x)))^2}{x^4} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(76\) vs. \(2(22)=44\).
time = 0.14, antiderivative size = 76, normalized size of antiderivative = 3.45, number of steps
used = 18, number of rules used = 4, integrand size = 52, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {14, 2404,
2341, 2342} \begin {gather*} \frac {3572100}{x^4}+\frac {893025 \log ^2(x)}{x^4}-\frac {3572100 \log (x)}{x^4}+\frac {3095820}{x^3}+\frac {595350 \log ^2(x)}{x^3}-\frac {2738610 \log (x)}{x^3}+\frac {908901}{x^2}+\frac {99225 \log ^2(x)}{x^2}-\frac {635040 \log (x)}{x^2}+\frac {103194}{x}-\frac {39690 \log (x)}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2341
Rule 2342
Rule 2404
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {23814 \left (750+505 x+103 x^2+6 x^3\right )}{x^5}+\frac {39690 (3+x) \left (135+34 x+x^2\right ) \log (x)}{x^5}-\frac {198450 (3+x) (6+x) \log ^2(x)}{x^5}\right ) \, dx\\ &=-\left (23814 \int \frac {750+505 x+103 x^2+6 x^3}{x^5} \, dx\right )+39690 \int \frac {(3+x) \left (135+34 x+x^2\right ) \log (x)}{x^5} \, dx-198450 \int \frac {(3+x) (6+x) \log ^2(x)}{x^5} \, dx\\ &=-\left (23814 \int \left (\frac {750}{x^5}+\frac {505}{x^4}+\frac {103}{x^3}+\frac {6}{x^2}\right ) \, dx\right )+39690 \int \left (\frac {405 \log (x)}{x^5}+\frac {237 \log (x)}{x^4}+\frac {37 \log (x)}{x^3}+\frac {\log (x)}{x^2}\right ) \, dx-198450 \int \left (\frac {18 \log ^2(x)}{x^5}+\frac {9 \log ^2(x)}{x^4}+\frac {\log ^2(x)}{x^3}\right ) \, dx\\ &=\frac {4465125}{x^4}+\frac {4008690}{x^3}+\frac {1226421}{x^2}+\frac {142884}{x}+39690 \int \frac {\log (x)}{x^2} \, dx-198450 \int \frac {\log ^2(x)}{x^3} \, dx+1468530 \int \frac {\log (x)}{x^3} \, dx-1786050 \int \frac {\log ^2(x)}{x^4} \, dx-3572100 \int \frac {\log ^2(x)}{x^5} \, dx+9406530 \int \frac {\log (x)}{x^4} \, dx+16074450 \int \frac {\log (x)}{x^5} \, dx\\ &=\frac {27683775}{8 x^4}+\frac {2963520}{x^3}+\frac {1718577}{2 x^2}+\frac {103194}{x}-\frac {8037225 \log (x)}{2 x^4}-\frac {3135510 \log (x)}{x^3}-\frac {734265 \log (x)}{x^2}-\frac {39690 \log (x)}{x}+\frac {893025 \log ^2(x)}{x^4}+\frac {595350 \log ^2(x)}{x^3}+\frac {99225 \log ^2(x)}{x^2}-198450 \int \frac {\log (x)}{x^3} \, dx-1190700 \int \frac {\log (x)}{x^4} \, dx-1786050 \int \frac {\log (x)}{x^5} \, dx\\ &=\frac {3572100}{x^4}+\frac {3095820}{x^3}+\frac {908901}{x^2}+\frac {103194}{x}-\frac {3572100 \log (x)}{x^4}-\frac {2738610 \log (x)}{x^3}-\frac {635040 \log (x)}{x^2}-\frac {39690 \log (x)}{x}+\frac {893025 \log ^2(x)}{x^4}+\frac {595350 \log ^2(x)}{x^3}+\frac {99225 \log ^2(x)}{x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 43, normalized size = 1.95 \begin {gather*} \frac {3969 \left (900+780 x+229 x^2+26 x^3-10 (3+x)^2 (10+x) \log (x)+25 (3+x)^2 \log ^2(x)\right )}{x^4} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(76\) vs.
\(2(23)=46\).
time = 0.02, size = 77, normalized size = 3.50
method | result | size |
risch | \(\frac {99225 \left (x^{2}+6 x +9\right ) \ln \left (x \right )^{2}}{x^{4}}-\frac {39690 \left (x^{3}+16 x^{2}+69 x +90\right ) \ln \left (x \right )}{x^{4}}+\frac {103194 x^{3}+908901 x^{2}+3095820 x +3572100}{x^{4}}\) | \(59\) |
norman | \(\frac {3572100+3095820 x +908901 x^{2}+103194 x^{3}+893025 \ln \left (x \right )^{2}-2738610 x \ln \left (x \right )+595350 x \ln \left (x \right )^{2}-635040 x^{2} \ln \left (x \right )+99225 x^{2} \ln \left (x \right )^{2}-39690 x^{3} \ln \left (x \right )-3572100 \ln \left (x \right )}{x^{4}}\) | \(65\) |
default | \(\frac {99225 \ln \left (x \right )^{2}}{x^{2}}-\frac {635040 \ln \left (x \right )}{x^{2}}+\frac {908901}{x^{2}}-\frac {39690 \ln \left (x \right )}{x}+\frac {103194}{x}+\frac {595350 \ln \left (x \right )^{2}}{x^{3}}-\frac {2738610 \ln \left (x \right )}{x^{3}}+\frac {3095820}{x^{3}}+\frac {893025 \ln \left (x \right )^{2}}{x^{4}}-\frac {3572100 \ln \left (x \right )}{x^{4}}+\frac {3572100}{x^{4}}\) | \(77\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 100 vs.
\(2 (19) = 38\).
time = 0.26, size = 100, normalized size = 4.55 \begin {gather*} -\frac {39690 \, \log \left (x\right )}{x} + \frac {99225 \, {\left (2 \, \log \left (x\right )^{2} + 2 \, \log \left (x\right ) + 1\right )}}{2 \, x^{2}} + \frac {103194}{x} - \frac {734265 \, \log \left (x\right )}{x^{2}} + \frac {66150 \, {\left (9 \, \log \left (x\right )^{2} + 6 \, \log \left (x\right ) + 2\right )}}{x^{3}} + \frac {1718577}{2 \, x^{2}} - \frac {3135510 \, \log \left (x\right )}{x^{3}} + \frac {893025 \, {\left (8 \, \log \left (x\right )^{2} + 4 \, \log \left (x\right ) + 1\right )}}{8 \, x^{4}} + \frac {2963520}{x^{3}} - \frac {8037225 \, \log \left (x\right )}{2 \, x^{4}} + \frac {27683775}{8 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 51 vs.
\(2 (19) = 38\).
time = 0.36, size = 51, normalized size = 2.32 \begin {gather*} \frac {3969 \, {\left (26 \, x^{3} + 25 \, {\left (x^{2} + 6 \, x + 9\right )} \log \left (x\right )^{2} + 229 \, x^{2} - 10 \, {\left (x^{3} + 16 \, x^{2} + 69 \, x + 90\right )} \log \left (x\right ) + 780 \, x + 900\right )}}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 61 vs.
\(2 (20) = 40\).
time = 0.12, size = 61, normalized size = 2.77 \begin {gather*} \frac {\left (99225 x^{2} + 595350 x + 893025\right ) \log {\left (x \right )}^{2}}{x^{4}} - \frac {- 103194 x^{3} - 908901 x^{2} - 3095820 x - 3572100}{x^{4}} + \frac {\left (- 39690 x^{3} - 635040 x^{2} - 2738610 x - 3572100\right ) \log {\left (x \right )}}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 58 vs.
\(2 (19) = 38\).
time = 0.39, size = 58, normalized size = 2.64 \begin {gather*} \frac {99225 \, {\left (x^{2} + 6 \, x + 9\right )} \log \left (x\right )^{2}}{x^{4}} - \frac {39690 \, {\left (x^{3} + 16 \, x^{2} + 69 \, x + 90\right )} \log \left (x\right )}{x^{4}} + \frac {3969 \, {\left (26 \, x^{3} + 229 \, x^{2} + 780 \, x + 900\right )}}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.91, size = 62, normalized size = 2.82 \begin {gather*} \frac {x\,\left (893025\,{\ln \left (x\right )}^2-3572100\,\ln \left (x\right )+3572100\right )+x^3\,\left (99225\,{\ln \left (x\right )}^2-635040\,\ln \left (x\right )+908901\right )+x^2\,\left (595350\,{\ln \left (x\right )}^2-2738610\,\ln \left (x\right )+3095820\right )-x^4\,\left (39690\,\ln \left (x\right )-103194\right )}{x^5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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